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A study on nonlinear steady-state waves at resonance in water of finite depth by the amplitude-based homotopy analysis method

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Abstract

Nonlinear steady-state waves are obtained by the amplitude-based homotopy analysis method (AHAM) when resonances among surface gravity waves are considered in water of finite depth. AHAM, newly proposed in this paper within the context of homotopy analysis method (HAM) and well validated in various ways, is able to deal with nonlinear wave interactions. In waves with small propagation angles, it is confirmed that more components share the wave energy if the wave field has a greater steepness. However, in waves with larger propagation angles, it is newly found that wave energy may also concentrate in some specific components. In such wave fields, off-resonance detuning is also considered. Bifurcation and symmetrical properties are discovered in some wave fields. Our results may provide a deeper understanding on nonlinear wave interactions at resonance in water of finite depth.

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Acknowledgements

The author Da-li Xu would like to thank Prof. Michael Stiassnie (Technion-Israel Institute of Technology) for the discussions on Zakharov equation.

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Authors and Affiliations

  1. College of Ocean Science and Engineering, Shanghai Maritime University, Shanghai, 201306, China

    Da-li Xu

  2. School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China

    Zeng Liu

Authors
  1. Da-li Xu
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  2. Zeng Liu
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Corresponding author

Correspondence to Da-li Xu.

Additional information

Project supported by the National Nature Science Foundation of China (Grant Nos. 11602136, 51609090), the Science and Technology Commission of Shanghai Municipality (Grant No. 17040501600).

Biography

Da-li Xu (1986-), Female, Ph. D., Lecturer

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Xu, Dl., Liu, Z. A study on nonlinear steady-state waves at resonance in water of finite depth by the amplitude-based homotopy analysis method. J Hydrodyn 32, 888–900 (2020). https://doi.org/10.1007/s42241-020-0013-5

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  • DOI: https://doi.org/10.1007/s42241-020-0013-5

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